Question: Rewrite as a simplified fraction. ${2.1\overline{28} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2128.2828...\\ 10x &= 21.2828...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2107}$ ${x = \dfrac{2107}{990}} \text{or} {2 \dfrac{127}{990}}$